Let $g(x)=\dfrac{1}{x^{10}}$. $g'(x)=$
Answer: The strategy We can first rewrite $g(x)$ as a negative power of $x$. Then, the derivative of $g$ can be found using the power rule : $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$ (Remember that this applies even when $n$ is negative.) Rewriting the fraction as a negative power $g(x)=\dfrac{1}{x^{10}}=x^{-10}$ Differentiating using the power rule $\begin{aligned} &\phantom{=}g'(x) \\\\ &=\dfrac{d}{dx}\left(x^{-10}\right) \\\\ &=-10x^{-10-1} \gray{\text{The power rule}} \\\\ &=-10x^{-11} \end{aligned}$ In conclusion, we found that $g'(x)=-10x^{-11}$. This can also be written as $-\dfrac{10}{x^{11}}$ (all equivalent forms are accepted).